Metrics for VandenBroeck and Keller, Equation (6)

analyze273.0ms (6.7%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
0%	0%	99.9%	0.1%	0%	0%	0%	6
21.9%	21.9%	78%	0.1%	0%	0%	0%	7
23.4%	23.4%	76.5%	0.1%	0%	0%	0%	8
35.2%	35.1%	64.8%	0.1%	0%	0%	0%	9
36.3%	36.3%	63.6%	0.1%	0%	0%	0%	10
42.4%	42.3%	57.6%	0.1%	0%	0%	0%	11
43.1%	43%	56.9%	0.1%	0%	0%	0%	12

Compiler

Compiled 17 to 11 computations (35.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 126.0ms

ival-mult: 60.0ms (47.8% of total)

ival-tan: 20.0ms (15.9% of total)

ival-div: 17.0ms (13.5% of total)

ival-pi: 14.0ms (11.2% of total)

ival-sub: 12.0ms (9.6% of total)

const: 3.0ms (2.4% of total)

sample2.8s (69.4%)

Results

1.2s	950×	2048	valid
590.0ms	1757×	1024	valid
398.0ms	4826×	256	valid
152.0ms	47×	4096	valid
146.0ms	676×	512	valid
3.0ms	5×	8192	exit

Precisions

Click to see histograms. Total time spent on operations: 2.1s

ival-tan: 1.4s (68.6% of total)

ival-mult: 356.0ms (17.2% of total)

ival-div: 125.0ms (6% of total)

ival-sub: 83.0ms (4% of total)

ival-pi: 68.0ms (3.3% of total)

const: 18.0ms (0.9% of total)

Bogosity

preprocess316.0ms (7.8%)

Algorithm

1×	egg-herbie

Rules

394×	`fma-define`
301×	`times-frac`
209×	`fma-neg`
96×	`associate-r`
87×	`associate-/r*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	415
1	97	357
2	270	357
3	708	357
4	1312	357
5	1876	357
6	2255	357
7	2424	357
8	2435	357

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) l))))
(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) l))))
(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 F) (neg.f64 F))) (tan.f64 (.f64 (PI.f64) l))))
(-.f64 (.f64 (PI.f64) (neg.f64 l)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) (neg.f64 l)))))
(neg.f64 (-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 F) (neg.f64 F))) (tan.f64 (.f64 (PI.f64) l)))))
(neg.f64 (-.f64 (.f64 (PI.f64) (neg.f64 l)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) (neg.f64 l))))))
(-.f64 (.f64 (PI.f64) F) (.f64 (/.f64 #s(literal 1 binary64) (.f64 l l)) (tan.f64 (.f64 (PI.f64) F))))

Outputs
(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) l))))
(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
(fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F (neg.f64 F))))
(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) l))))
(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
(fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F (neg.f64 F))))
(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 F) (neg.f64 F))) (tan.f64 (.f64 (PI.f64) l))))
(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) l))))
(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
(fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F (neg.f64 F))))
(-.f64 (.f64 (PI.f64) (neg.f64 l)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) (neg.f64 l)))))
(fma.f64 (PI.f64) (neg.f64 l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))
(-.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) (*.f64 (PI.f64) l))
(neg.f64 (-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 F) (neg.f64 F))) (tan.f64 (.f64 (PI.f64) l)))))
(-.f64 (.f64 (PI.f64) (neg.f64 l)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) (neg.f64 l)))))
(fma.f64 (PI.f64) (neg.f64 l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))
(-.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) (*.f64 (PI.f64) l))
(neg.f64 (-.f64 (.f64 (PI.f64) (neg.f64 l)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) (neg.f64 l))))))
(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) l))))
(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
(fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F (neg.f64 F))))
(-.f64 (.f64 (PI.f64) F) (.f64 (/.f64 #s(literal 1 binary64) (.f64 l l)) (tan.f64 (.f64 (PI.f64) F))))
(-.f64 (.f64 (PI.f64) F) (/.f64 (/.f64 (tan.f64 (.f64 (PI.f64) F)) l) l))
(-.f64 (.f64 (PI.f64) F) (/.f64 (tan.f64 (.f64 (PI.f64) F)) (*.f64 l l)))

Symmetry

(abs F)

(negabs l)

explain616.0ms (15.2%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
124	-	-	`(tan.f64 (*.f64 (PI.f64) l))`
46	-	-	`(.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (*.f64 (PI.f64) l)))`
1	-	-	`(/.f64 #s(literal 1 binary64) (*.f64 F F))`
0	-	-	`(PI.f64)`
0	-	-	`F`
0	-	-	`l`
0	-	-	`(*.f64 F F)`
0	-	-	`(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) l))))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(*.f64 (PI.f64) l)`

Results

376.0ms	104×	4096	valid
154.0ms	138×	2048	valid
31.0ms	270×	256	valid

Compiler

Compiled 108 to 32 computations (70.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 490.0ms

ival-tan: 431.0ms (88% of total)

ival-mult: 32.0ms (6.5% of total)

ival-div: 12.0ms (2.4% of total)

ival-sub: 7.0ms (1.4% of total)

ival-pi: 6.0ms (1.2% of total)

const: 2.0ms (0.4% of total)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	75.5%	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) l))))

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`neg-mul-1`
12×	`unsub-neg`
9×	`*-commutative`
8×	`distribute-lft-neg-in`
8×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	57
1	28	57
2	43	57
3	56	57
4	68	57
5	93	57
6	127	57
7	129	57

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 #s(literal 1 binary64) (.f64 F F)) (tan.f64 (.f64 (PI.f64) l))))

Outputs

(-.f64 (*.f64 (PI.f64) l) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 F F)) (tan.f64 (*.f64 (PI.f64) l))))

(+.f64 (*.f64 (PI.f64) l) (*.f64 (tan.f64 (*.f64 (PI.f64) l)) (/.f64 #s(literal -1 binary64) (*.f64 F F))))

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 16 to 10 computations (37.5% saved)

preprocess28.0ms (0.7%)

Remove

(negabs l)

(abs F)

Compiler

Compiled 192 to 120 computations (37.5% saved)

VandenBroeck and Keller, Equation (6)

analyze273.0ms (6.7%)

sample2.8s (69.4%)

preprocess316.0ms (7.8%)

explain616.0ms (15.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.2%)

soundness0.0ms (0%)

preprocess28.0ms (0.7%)

end0.0ms (0%)

Profiling